Combination Chemotherapy and Rituximab in Treating Young Patients With Recurrent or Refractory Non-Hodgkin's Lymphoma or Acute Lymphoblastic Leukemia

Inclusion Criteria: * Histologically confirmed B-cell non-Hodgkin's lymphoma OR acute lymphoblastic leukemia * CD20+ (confirmed by flow cytometry of tumor tissue, involved marrow, or CD20 immunostaining) * The following histologies are generally CD20+ and are eligible: * Diffuse large B-cell lymphoma, mediastinal (thymic) large B-cell lymphoma, or follicular lymphoma, grade III (rare), documented by flow cytometry or appropriate immunohistochemistry, any stage * Burkitt's lymphoma or atypical Burkitt's/Burkitt-like lymphoma, any stage * B-cell acute lymphoblastic leukemia, with FABL3 morphology and/or demonstration of surface immunoglobin by flow cytometry * Atypical precursor B-cell lymphoblastic lymphoma or other unusual histologies that are CD20+ * Measurable disease by clinical, radiographic, or histologic criteria * Must be in first or later recurrence or have disease that is primarily refractory to conventional therapy * No isolated CNS disease * Performance status - ECOG 0-2 * At least 2 months * Absolute neutrophil count ≥ 1,000/mm\^3\* * Platelet count ≥ 100,000/mm\^3 (transfusion independent)\* * Hemoglobin ≥ 10.0 g/dL (RBC transfusion allowed)\* * Bilirubin ≤ 1.5 times normal * ALT \< 2.5 times normal * No chronic renal insufficiency * Renal insufficiency allowed provided it is secondary to tumor lysis syndrome * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 3 months after study treatment * HIV negative * No active uncontrolled infection * Seizure disorder allowed if well controlled with anticonvulsants * No CNS toxicity greater than grade II * At least 24 hours since prior growth factor(s) * At least 60 days since prior biologic (antineoplastic) therapy * Prior stem cell transplantation allowed provided the following criteria are met: * More than 60 days since transplantation * Hematopoietic lab value requirements are met (See Hematopoietic) * No evidence of graft-versus-host disease (if post-allogeneic transplantation) * Prior monoclonal antibody therapy allowed (including rituximab) * No other concurrent immunomodulating agents * More than 2 weeks since prior myelosuppressive chemotherapy (4 weeks for nitrosoureas) * No other concurrent chemotherapy * No concurrent steroids (except for rituximab infusion-related symptoms) * At least 2 weeks since prior local palliative radiotherapy (small port) * At least 6 weeks since prior substantial bone marrow radiotherapy * At least 6 months since prior craniospinal radiotherapy or radiotherapy to 50% or more of the pelvis * Concurrent radiotherapy to localized painful, airway-compromising, or other acute organ-threatening lesions allowed provided at least 1 measurable lesion is not irradiated * Recovered from prior therapy * No concurrent participation in another phase II study